"tired" and "bored" are exceptions to the rule. They are di-syllabic words (i.e., they each have two syllables, or they can be read that way) which makes them compatible with comparative "more":
EX: "tired" has two syllables (tai ' rd), so "more tired".
EX: "bored" has two syllables (bo ' [w]rd), so "more bored".
The 2nd syllable 'rd is somewhat of a maverick. You see, "r" is not a vowel, but it does have vowel-like properties, so it either functions as the syllable's nucleus (i.e., tai'rd, bo'[w]rd) or it colors the vowel before it (i.e., bord), or it does both. That is, mono-syllablic, bord and di-syllabic, bo'[w]rd). So, rd, not -ed, is subject to interpretation. The "e" of -ed is not pronounced in "tired" or "bored". It's silent.
"tired" has only one vowel (taird), which makes it a mono-syllabic word, so "tireder", not "more tired".
"tired" has two vocalic sounds (tai'rd), which makes it a di-syllabic word, so "more tired", not "tireder".
"bored" has one vowel (bord), so "boreder".
"bored" has two vocalic sounds (bo'[w]rd), so "more bored"
In short, if you pronounce "bored" as one syllable, then it takes comparative -er; if you pronounce "bored" as two syllables, then it takes comparative "more".
Check here also (scroll down to the middle of the page):
Furthemore, distribution also plays a part:
EX: If I get any more tired than I am now, I'll be (even) tireder.
"more tired than" expresses a comparison structurally, whereas "tireder" doesn't:
Comparison (X & Y): X = more . . . than Y
Adjective (X, no Y): X = (even) -er.
Speakers also alternate the forms:
EX: I feel even more bored now than I did before.
EX: I feel even boreder now than I did before.